1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integral of Composition Functions

  1. Oct 23, 2012 #1
    1. The problem statement, all variables and given/known data

    http://sphotos-h.ak.fbcdn.net/hphotos-ak-snc6/282312_368248176595083_1229435302_n.jpg [Broken]

    2. Relevant equations

    To subtitute x into U, but that did not work.

    3. The attempt at a solution

    I have tried subtituting x into U like this :

    http://sphotos-g.ak.fbcdn.net/hphotos-ak-snc7/578486_368249266594974_1874868606_n.jpg [Broken]

    The last two lines are my "goofing around" answer. :tongue2:
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Oct 23, 2012 #2
    If you change variables, you have to change them all! You can't just leave some x's laying around. Now you have x=x(u) and you don't know how this integrates.

    There is kind of a standard trick for any integral that looks like this, which is to first complete the square. What you want to do is to write the integrand into a form
    [tex] \frac{dx}{\sqrt{A^2 - (B+Cx)^2}} [/tex]
    and then do a trigonometric substitution [itex]B+Cx = A \sin t [/itex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook